Neural network based helicopter low airspeed indicator

ABSTRACT

The invention is directed to means, utilizing a neural network, for estimating helicopter airspeed at speeds below about 50 knots using only fixed system parameters as inputs to the neural network. The system includes: means for entering at least one initial parameter; means for measuring, in a nonrotating reference frame associated with the helicopter, a plurality of variable state parameters generated during flight of the helicopter; means for determining a plurality of input parameters based on the at least one initial parameter and the plurality of variable state parameters and for generating successive signals representing the input parameters; at least one equation representing a nonlinear input-output relationship between the input parameters and airspeed; memory means for storing the at least one equation and for successively receiving and storing signals from the determining means; and processing means responsive to signals received from the memory means for generating airspeed information based on the input parameters and the at least one equation.

STATEMENT OF GOVERNMENT RIGHTS

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to virtual sensors and, moreparticularly, to a means and method utilizing a neural network forestimating helicopter airspeed at speeds below about 50 knots using onlyfixed system parameters (i.e., parameters measured or determined in areference frame fixed relative to the helicopter fuselage) as inputs tothe neural network.

2. Brief Description of Related Art

Helicopters are designed for a wide variety of missions includinganti-submarine warfare, vertical replenishment, and search and rescuemissions. Although helicopters routinely operate at forward airspeedsabove 100 knots, such missions require that a large portion of flighttime be conducted in the low airspeed flight regime (i.e., airspeedsbelow about 50 knots). Because flight in the low airspeed regimerequires increased power, accurate low airspeed data is needed tomaintain control margins. Low airspeed data is needed by pilots flyinginstrument approaches in order to maintain critical control authority,particularly in connection with tail-rotor effectiveness. On attackhelicopters, low airspeed information is critical to accurate weaponsfiring solutions. In addition, high vibratory loads can occur in somelow airspeed maneuvers resulting in fatigue damage accumulation inflight critical components. Technology for monitoring the safe liferemaining on such flight critical components has been developed throughhelicopter usage monitoring and flight regime recognition techniques,e.g., Health and Usage Monitoring Systems (HUMS). Normally, informationfrom multiple sensors must be examined collectively to make diagnosticand prognostic decisions. However, the success of HUMS technology in thelow airspeed regime is dependent on accurate low airspeed information.Without correct low airspeed information, usage monitoring algorithmscannot recognize the low airspeed maneuvers and, therefore, may notregister critical fatigue accumulation data.

Due to inaccuracy associated with use of traditional pitot-static probesin a low airspeed environment, as well as with interference generated bythe main rotor downwash, instrumentation for accurately measuringairspeed and sideslip angle in the low airspeed regime is generallylacking. Thus, although accurate low airspeed information is needed bypilots and monitoring algorithms, it is not available using traditionalmethods of measuring airspeed and sideslip angle.

Development of a measurement system that accurately estimates lowairspeed and sideslip angle has long been a difficult challenge.Interest in low airspeed measurement began in the 1950s when preliminaryconcepts were developed and flight tested. These concepts involvedmounting probes above the rotor hub as well as in the wake beneath therotor. Since the 1950s, these concepts have been refined and a varietyof low airspeed sensor designs have been flight tested. One such systememploys two venturi tubes on opposite ends of a rotating arm installedabove the rotor hub to measure true airspeed magnitude and direction,e.g., LORAS (Low Range Airspeed System) produced by the Pacer Company ofthe United States. The differential pressure between the two sensors isused to calculate the airspeed and sideslip angle. Such systems,however, require slip ring assemblies or some other means oftransferring data from the rotating reference frame of the rotor to thefixed (i.e., nonrotating) reference frame of the fuselage. Anotherapproach involves a sensor designed to be mounted under the rotorwherein the nature of the wake is used to determine helicopter airspeed,e.g., LASSIE (Low Air Speed Sensing and Indicating System) produced bythe GEC Company of England. This system uses a pitot-static probe whichcan rotate about 360° to provide airspeed and sideslip angleinformation. However, the flow environment under the rotor system iscomplex and empirical methods are used to linearize the output. Severalother techniques, including those using ultrasonic transmission timesand shed vortex characteristics, have been proposed for deducing lowairspeed and sideslip angle information.

The search for an effective low airspeed sensor has long been adifficult challenge for the helicopter R&D sector. Few proposedsolutions have made it into use. Most proposed low airspeed measurementsystems are externally mounted and require transferring information froma reference frame rotating with the rotor to a reference frame fixedrelative to the helicopter fuselage (i.e., a helicopter fixed system ofcoordinates XYZ originating in the helicopter fuselage). Due to themechanical complexity, expense, and increased drag introduced byproposed low airspeed measurement systems, most helicopters are notequipped with low airspeed sensors. Moreover, in many cases, physicalsensors cannot be affordably and reliably applied in an operationalenvironment on military helicopters. Thus, the vast majority ofcommercial and military helicopters in use today do not have an airspeedsystem that can accurately measure airspeed below about 50 knots eventhough this is within the flight regime of the helicopter. Generally,investment in low airspeed measurement equipment is reserved for thoseaircraft with a critical low airspeed mission. Consequently, there is aneed for a simple, low cost means and method for determining lowairspeed and sideslip angle experienced by the helicopter.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide a meansand method for simply, accurately, and economically determininghelicopter low airspeed information (i.e., airspeed and sideslip anglebelow about 50 knots).

It is a further object of the present invention to provide a means andmethod for determining helicopter low airspeed using only inputparameters derived in the fixed reference frame of the helicopterfuselage.

It is still a further object of the present invention to provide a meansand method employing existing flight sensors supplying fixed frameparameters to a neural network for estimating low airspeed.

It is yet a further object of the present invention to provide a meansand method for determining helicopter low airspeed capable of beingembedded into a helicopter's existing flight data recording system.

Other objects and advantages of the present invention will becomeapparent to those skilled in the art upon a reading of the followingdetailed description taken in conjunction with the drawings and theclaims supported thereby.

In accordance with one embodiment of the present invention, theseobjects are met by providing a virtual sensor for estimating lowairspeed of a helicopter. The virtual sensor includes: determining meansfor determining a plurality of input parameters; at least one neuralnetwork equation representing a learned nonlinear relationship betweenthe input parameters and airspeed; memory means operatively coupled tothe determining means for receiving and storing the input parameters andthe at least one neural network equation; and processing meansoperatively coupled to the memory means. The plurality of inputparameters are determined, and continuously updated at a sampling rate,during low airspeed flight of the helicopter. The processing meansreceives the input parameters from the memory means and provides a lowairspeed signal in response to the input parameters and the at least oneneural network equation. The virtual sensor may further include displaymeans operatively coupled to the processing means for receiving the lowairspeed signal from the processing means and providing an indication ofthe low airspeed to the crew and/or aircraft monitoring system.

The at least one neural network equation includes at least one airspeedequation representing a nonlinear input-output relationship between theplurality of input parameters and low airspeed and operative fordetermining low airspeed based upon the plurality of input parameters.The at least one airspeed equation is derived by means of a neuralnetwork that has been trained using training exemplars corresponding tothe plurality of input parameters and a coinciding reference speed ofthe helicopter. The training exemplars are determined at a plurality oftest flight conditions representing a predefined low airspeed flightdomain of the helicopter.

The at least one neural network equation may further include at leastone sideslip equation representing a nonlinear input-output relationshipbetween the input parameters and a sideslip angle of the helicopter andoperative for determining the sideslip angle or classifying the sideslipangle into one of four quadrants. The at least one sideslip equation isderived by means of a neural network that has been trained with aplurality of training exemplars that correspond to the input parameters,a coinciding reference speed of the helicopter and a coinciding sideslipangle derived from the coinciding reference speed. The trainingexemplars are measured at multiple test flight conditions representing apredetermined low airspeed flight domain of the helicopter.

The means for determining a plurality of input parameters includes meansfor determining: helicopter gross weight; helicopter center of gravity;longitudinal cyclic stick position; lateral cyclic stick position;collective stick position; pilot pedal position; pitch attitude; rollattitude; pitch rate; roll rate; yaw rate; at least one engine torque;at least one rotor rotational speed; and helicopter altitude.

In accordance with a further embodiment of the present invention, asystem is provided for estimating airspeed of a helicopter operating atairspeeds below about 50 knots in response to variable state parametersgenerated during flight of the helicopter. The system includes:inputting means for entering at least one initial parameter; means formeasuring, in a nonrotating reference frame associated with thehelicopter, a plurality of variable state parameters; means forcalculating a plurality of input parameters based on the at least oneinitial parameter and the plurality of variable state parameters and forgenerating successive signals representing the input parameters; atleast one equation representing a nonlinear input-output relationshipbetween the input parameters and airspeed; memory means for storing theat least one equation and for successively receiving and storing signalsfrom the means for calculating; and processing means responsive tosignals received from the memory means for generating airspeedinformation based on the input parameters and the at least one equation.Airspeed of the helicopter is estimated in a real time fashion bycontinuously updating, at a predetermined sampling rate during lowairspeed flight, the measurement of the plurality of variable stateparameters.

The nonlinear input-output relationship is determined using a neuralnetwork that has been trained with training exemplars corresponding tothe plurality of input parameters and a coinciding reference speed ofthe helicopter. The training exemplars are determined at a plurality offlight conditions representative of a flight domain experienced by thehelicopter below about 50 knots.

The at least one initial parameter includes helicopter weight and centerof gravity position at takeoff. The measuring means includes sensors forsampling the variable state parameters at the predetermined samplingrate. The sensors include sensors for measuring: fuel expended duringflight; longitudinal cyclic stick position; lateral cyclic stickposition; collective stick position; pedal position; pitch rate; rollrate; yaw rate; at least one engine torque; at least one rotorrotational speed; and static pressure and/or temperature of thesurrounding air.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing objects and other advantages of the present invention willbe more fully understood by reference to the following description takenin conjunction with the accompanying drawings wherein like referencenumerals refer to like or corresponding elements throughout and wherein:

FIG. 1 is a symbolic representation of one embodiment of the presentinvention installed on a helicopter;

FIG. 2 is a flow chart of a method for practicing the present invention;

FIG. 3 shows the four quadrants for classifying sideslip angle inaccordance with the present invention;

FIG. 4 represents a typical data set for training or testing the neuralnetworks in accordance with the present invention;

FIG. 5 presents preliminary airspeed predictions using a test data setcontaining both in and out of ground effect data;

FIG. 6A and 6B present airspeed predictions using test and training datasets, respectively, containing out of ground effect data only;

FIG. 7 presents airspeed predictions using a test data set containing inground effect data only; and

FIG. 8 presents airspeed predictions using a linear model and a testdata set containing out of ground effect data.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention provides means and method that utilize neuralnetwork technology for estimating helicopter low airspeed (i.e.,airspeed below about 50 knots) using parameters measured or determinedin a reference frame fixed relative to the helicopter fuselage as inputsto the neural network. Airspeed is a measure of the helicopter'svelocity relative to the surrounding air. One embodiment of the presentinvention provides a virtual sensor employing advanced neural networksfor estimating helicopter low airspeed in a real time fashion. A furtherembodiment of the present invention provides a system for estimatingairspeed of a helicopter below about 50 knots in response to variablestate parameters generated during flight of the helicopter and measuredin the fixed (i.e., nonrotating) reference frame associated with thehelicopter. A still further embodiment of the present invention providesa method for estimating real time airspeed of a helicopter operatingbelow about 50 knots. Additionally, the present invention can be used todetermine sideslip angle of a helicopter operating at low airspeeds.Certain aspects of the present invention are presented in: McCool, KellyM., David J. Haas and Carl G. Schaefer, Jr., "A Neural Network BasedApproach to Helicopter Low Airspeed and Sideslip Angle Estimation,"Proceedings of American Institute of Aeronautics and Astronautics FlightSimulation Technologies Conference, Paper No. 96-3481 (Jul. 29-31, 1996)pp. 91-101, incorporated herein by reference.

Referring now to the drawings, and particularly to FIG. 1, whichsymbolically depicts the present invention installed onboard helicopter10. Virtual sensor 11 in accordance with the present invention includes:determining means 12 for determining input parameters and for generatingsuccessive signals representing the input parameters; at least oneequation representing a nonlinear input-output relationship between theinput parameters and a desired output, e.g., low airspeed or sideslipangle; memory means 14 for storing the at least one equation and forsuccessively receiving (and optionally storing) signals from determiningmeans 12; and processing means 16 operatively coupled to memory means 14and responsive to signals received from memory means 14 for generatingdesired output signals based on the input parameters and the at leastone equation. Determining means 12 preferably includes input means 18for entering initial parameters, measuring means 20a through 20x formeasuring variable state parameters, and means 22 for calculating theinput parameters based on the initial parameters and the variable stateparameters. Input means 18 may be used to enter initial parameters intomemory 14 and/or into means 22 for calculating the input parameters.With respect to measuring means 20a-20x, x indicates the number ofmeasuring means used to measure the variable state parameters. Eachmeasuring means 20a-20x generates signals representing values of theparticular variable state parameter measured and transmits the signalsto memory 14 and/or to means 22 for calculating the input parameters.The invention may further include display means 24 operatively coupledto processing means 16 for receiving the desired output signals fromprocessing means 16 and for providing an indication of the desiredoutput in response thereto.

Determining means 12 derives input parameters from the entered initialparameters and the variable state parameters measured during low speedflight. Desired output, e.g., helicopter airspeed, is estimated in areal time fashion by continuously updating, at a predetermined samplingrate, measured values of the variable state parameters and calculatedvalues of the input parameters for input into processing means 16.Appropriate sampling rates may be from 1 to 20 samples per second (Hz)and preferably about 8 to 10 Hz.

As shown in Table 1 below, exemplary input parameters determined bydetermining means 12 for use with the present invention may include: (1)helicopter gross weight during flight; (2) helicopter center of gravityposition during flight; (3) longitudinal cyclic stick position; (4)lateral cyclic stick position; (5) collective stick position; (6) pilotpedal position; (7) pitch attitude; (8) roll attitude; (9) pitch rate;(10) roll rate; (11) yaw rate; (12) at least one engine torque (if thehelicopter has more than one engine, the torque of one or more of theengines may be measured and used as input parameters); (13) at least onerotor rotational speed (if the helicopter has more than one main rotor,the rotational speed of one or more of the rotors may be measured andused as input parameters); and (14) helicopter altitude.

Exemplary initial parameters may include the helicopter gross weight attakeoff (i.e., weight of helicopter, fuel, and cargo) and the helicoptercenter of gravity position at takeoff. Exemplary easily measurablevariable state parameters may include: (1) fuel expended during flight;(2) longitudinal cyclic stick position; (3) lateral cyclic stickposition; (4) collective stick position; (5) pilot pedal position; (6)pitch rate; (7) roll rate; (8) yaw rate; (9) engine torque(s); (10)rotor rotational speed(s); and (11) static pressure and/or temperatureof the surrounding air. Measuring means, 20a-20x, includes sensors,20a-20x, for sampling the variable state parameters at the predeterminedsampling rate.

The variable state parameters are an indication of pilot control inputsand helicopter response at a particular time during flight. The variablestate parameters are measured in a nonrotating reference frame fixedrelative to the helicopter fuselage (i.e., a helicopter fixed system ofcoordinates XYZ originating in the helicopter fuselage). Generally, thehelicopter fixed reference frame includes an X axis parallel to thehelicopter longitudinal (fore-aft) axis, a Y axis parallel to thehelicopter lateral (port-starboard) axis, and a vertical Z axisorthogonal to the X and Y axes. By only using parameters measured in thefixed system, or derived from parameters measured in the fixed system,the need for using complicated methods of transferring data from therotating system of the rotor to the fixed system of the fuselage isavoided. Most prior art systems require that such data be transferredfrom a rotating to a fixed system.

                  TABLE 1    ______________________________________    Input Parameter                  How Input Parameter is Determined    ______________________________________    Gross Weight  derived from takeoff gross weight minus                  measured weight of fuel burned    Center of Gravity                  derived from takeoff center of gravity                  and cg shift due to measured weight fuel                  burned    Longitudinal cyclic                  measured directly using position detector    stick position    Lateral cyclic                  measured directly using position detector    stick position    Collective stick                  measured directly using position detector    position    Pedal position                  measured directly using position detector    Pitch attitude                  derived by integrating measured pitch                  rate    Roll attitude derived by integrating measured roll rate    Pitch rate    measured directly using rate gyro    Roll rate     measured directly using rate gyro    Yaw rate      measured directly using rate gyro    Engine torque(s)                  measured directly using torque meter(s)    Rotor speed(s)                  measured directly using tachometer(s)    Altitude      derived from measured static pressure and                  or temperature    ______________________________________

In the preferred embodiment, memory means 14, processing means 16, inputmeans 18, means 22 for calculating the input parameters, and displaymeans 24 are components of an onboard computer system. For example,input means 18 is a computer keyboard, memory means 14 is at least onecomputer memory device (e.g., RAM and/or EPROM), processing means 16 andcalculating means 22 are one or more computer processors, and displaymeans 24 is a computer monitor. A software representation of the atleast one neural network equation is developed and installed into theonboard computer system as, for example, source code (e.g., C sourcecode) in a hard drive, Flash memory, or as an EPROM chip. Measuringmeans, 20a-20x, may comprise sensors installed for use with the presentinvention and/or may include existing flight data sensors alreadyonboard the helicopter. Preferably, the computer system and sensors arepart of a flight data recording system and/or automatic flight controlsystem onboard the helicopter.

Input parameters are determined during flight and entered or transmittedto the computer system for use with the source code representation ofthe neural network equations to estimate airspeed. As shown in Table 1,exemplary input parameters are determined as follows: (1) helicopteractual gross weight during flight is determined from the helicoptergross weight at takeoff (an initial parameter) minus the weight of fuelburned (derived from fuel expended which is a measured variable stateparameter measured, e.g., using a standard helicopter fuel gauge); (2)position of the center of gravity (cg) during flight is determined fromthe cg at take off (an initial parameter) and the cg shift due to weightof fuel expended; (3) longitudinal cyclic stick position, (4) lateralcyclic stick position, and (5) collective stick position are variablestate parameters measured directly using position detectors ortransducers for detecting the position of the cyclic or collectivestick, e.g., rotary or linear variable differential transformers formeasuring linear or angular displacement of the cyclic or collectivestick as a percentage of maximum displacement; (6) pilot pedal positionis a variable state parameter measured directly using position detectorsor transducers for detecting the position of the pedal, e.g., rotary orlinear variable differential transformers for measuring linear orangular displacement of the pedal as a percentage of maximumdisplacement; (7) pitch rate, (8) roll rate, and (9) yaw rate arevariable state parameters measured directly using, e.g., rate gyros(generally one gyro for each of pitch, roll and yaw); (10) pitchattitude and (11) roll attitude are derived by integrating measuredpitch rate and roll rate, respectively; (12) engine torque is a variablestate parameter measured directly using a torque meter; (13) rotor speedis a variable state parameter measured directly using a tachometer; and(14) altitude (pressure altitude or density altitude) is derived fromthe measured static pressure and/or temperature of air surrounding thehelicopter (a variable state parameter). Sensors 20a-20x for measuringthe variable state parameters and methods of obtaining derivedquantities are well known in the art and will not be discussed in detailherein.

In a preferred embodiment, the at least one equation includes at leastone airspeed equation representing a nonlinear input-output relationshipbetween the plurality of input parameters and airspeed and operative fordetermining low airspeed based upon the plurality of input parameters.The at least one airspeed equation is derived by means of a neuralnetwork that has been trained using training exemplars corresponding tothe plurality of input parameters and a coinciding reference speed ofthe helicopter. The training exemplars are determined at a plurality offlight conditions representing a predefined low airspeed flight domainof the helicopter (i.e., flight domain experienced by the helicopterbelow about 50 knots).

The at least one equation may further include at least one sideslipequation representing nonlinear input-output relationships between theinput parameters and a sideslip angle of the helicopter and operativefor determining sideslip angle or for classifying the sideslip angle ofthe helicopter into one of four quadrants. The at least one sideslipequation is derived by means of a neural network that has been trainedwith a plurality of training exemplars that correspond to the inputparameters, a coinciding reference speed of the helicopter and acoinciding sideslip angle derived from the coinciding reference speed.The training exemplars are measured at multiple flight conditionsrepresenting a predetermined low airspeed flight domain of thehelicopter.

In accordance with the present invention, neural network technology isemployed to estimate helicopter low airspeed and sideslip angle. Thatis, the at least one equation of the present invention is establishedusing neural networks. Use of neural network technology allows fornonlinear transfer between input parameters and airspeed whereasprevious analytical approaches for estimating helicopter low airspeedhave employed linear methods. The neural networks employed include aninput layer for receiving input parameters, an output layer foroutputting estimated airspeed or sideslip angle, and one or more hiddenlayers for mapping the input layer to the output layer through alearned, nonlinear input-output relationship. The networks are trained,and the nonlinear input-output relationships learned, based onmeasurable quantities (i.e., measured reference speed and easilymeasurable variable state parameters from which the input parameters arecalculated). One skilled in the art of neural networks could write asuitable program with the guidance provided herein. Additionally,commercially available neural network software packages may be used forpracticing the present invention. NeuralWare, a commercially availableneural network software package available from NeuralWare, Inc., 202Park West Dr., Pittsburgh, Pa. 15275, was used in developing the networkarchitecture of present invention. The neural network technology and howit is employed in the present invention is more fully described below.

The neural networks applicable to the present invention include, but arenot limited to, backpropagation neural networks, linear vectorquantization neural networks, modular neural networks, probabilisticneural networks, radial basis function neural networks, self organizingmaps, and recurrent neural networks. In one preferred embodiment, abackpropagation (BP) neural network is used to predict low airspeed anda linear vector quantization (LVQ) neural network is used to classifysideslip angle into one of four quadrants.

Referring to FIG. 2, a method (more fully described below) forpracticing the present invention is presented. Initially, as representedby boxes 30-34, a neural network is trained to develop nonlinearinput-output relationship between input variables and the desiredoutput. First, at 30, the user defines input parameters which may bederived from variable state parameters that are generated during flightof the helicopter and that are measured in the helicopter fixedreference frame. Next, at 32, training exemplars used to train thenetwork are determined. The training exemplars, which include the inputparameters and a corresponding desired output (i.e., airspeed orsideslip angle), are either directly measured during test flights or aredetermined based on parameters measured during test flights. The dataused to determine the training exemplars is measured at a plurality offlight conditions representing a predetermined low airspeed flightdomain of the helicopter. Then, at 34, the neural network learns aninput-output relationship between the input parameters and thecorresponding desired output. The input-output relationship isrepresented by at least one nonlinear equation. At 36, the at least onenonlinear equation is stored in a memory device onboard the helicopter.Once the input-output equations are installed onboard the helicopter,only the variable state parameters need be measured to estimatehelicopter airspeed during low airspeed operation At 38, initialparameters, used in calculating input parameters, are entered into amemory device onboard the helicopter. At 40, while the helicopter isoperating in the low airspeed range, onboard sensors measure variablestate parameters in the helicopter fixed reference frame. At 42, theinput parameters are calculated based on the entered initial parametersand the measured variable state parameters. The input parameters areoptionally stored, at 44, in a memory device onboard the helicopter. At46, the input parameters are processed in accordance with the at leastone nonlinear equation to determine the desired output. Finally, at 48,the desired output is displayed for use by occupants of the helicopterand/or is recorded by the aircraft monitoring system. By continuouslymeasuring the variable state parameters at a predetermined sampling rateduring low airspeed flight and then calculating and processing the inputparameters, the desired output is estimated and displayed in a real timefashion.

For purposes of training the neural network a plurality of trainingexemplar are determined over the expected flight domain of thehelicopter. With respect to estimating low airspeed, the trainingexemplars corresponds to the input parameters and a correspondingreference speed of the helicopter. With respect to determining orclassifying sideslip angle, the training exemplars corresponds to theinput parameters, a corresponding reference speed of the helicopter, anda corresponding sideslip angle. Actual helicopter low airspeed may bemeasured and used as the training exemplar reference speed. However,accurately measuring helicopter low airspeed is difficult, e.g., using apace aircraft equipped with a low airspeed sensing system such as aPacer (e.g., LORAS) low airspeed indicator. Therefore, helicoptervelocity relative to the ground measured during conditions of near zeroambient winds may be used as the reference speed of the helicopter. Whenmeasuring helicopter velocity relative to the ground, tests to determinenetwork training exemplars should be conducted only when prevailingwinds are near zero (preferably below 5 knots) in order to minimize thedifference between measured reference speed (relative to the ground) andtrue airspeed (relative to the surrounding air). Any well known methodof determining helicopter velocity, such as Doppler radar, GlobalPositioning Satellite (GPS) systems, or Laser tracking units, may beemployed and are within the scope of the present invention. Helicoptersideslip angle is derived from the measured reference speed which isbroken into velocity components in the forward (i.e., longitudinal orx-direction) and sideward (i.e., lateral or y-direction) directions.

Training the neural network results in one or more neural networkequations being learned. The one or more neural network equations arethen converted into computer language and are installed onboard thehelicopter. Once the one or more equations are installed in thehelicopter, only the input parameters need be determined (based oninitial parameters and easily measurable variable state parameters) toestimate the helicopter low airspeed and sideslip angle. The variablestate parameters may be measured (for purposes of network training orduring subsequent use for estimating low airspeed and sideslip angle)using, e.g., the well known sensors listed in Table 1.

Data set selection is a critical part of developing a successful set ofneural network architecture equations. Training exemplars for trainingthe neural network of the present invention will be selected anddetermined for any particular helicopter class or configuration forwhich the present invention is used (e.g., single rotor aircraft, tandemrotor aircraft, tilt rotor aircraft). Training exemplars should consistof data which fully represents the domain of the problem to be modeled.For example, the problem domain of the present invention is estimatingairspeed and/or sideslip angle of a helicopter during low airspeedflight. Consequently, the training exemplars should cover the range ofairspeed and sideslip combinations encountered in the low airspeedflight environment.

For low airspeed estimation in accordance with the present invention,the helicopter is preferably tested at airspeeds from hover to about 50knots over a full range of sideslip angles. Depending upon the knownflight envelop of a particular helicopter, steady flight data only maybe used when training the system or steady and accelerating flight datamay be used. The data set of training exemplars should not be weightedtoward any one flight condition as such weightings may result in neuralnetwork equations that estimate airspeed well in that condition but failin other maneuvers. In addition, factors which might significantlyaffect the input-output relationship represented by the networkequations must be considered. For example, it has been found that thelow airspeed indicator input-output relationship varies depending onwhether the helicopter is operating in ground effect (IGE) or out ofground effect (OGE). These factors were considered in developing atraining data set for the present invention.

As stated earlier, in one preferred embodiment of the present inventiontwo types of neural networks were employed. A backpropagation (BP)network is preferred for predicting helicopter low airspeed and a linearvector quantization (LVQ) network is preferred for quantifying sideslipangle. Generally, a BP network architecture consists of an input layer,one or more hidden layers, and an output layer. Each hidden layercontains one or more processing elements (PEs). At each PE a transferfunction with a corresponding connection weight is applied to develop arelationship between the input and output vectors. Transfer functionsmay be linear or nonlinear, however, nonlinear transfer functions arepreferred. LVQ network architecture consists of an input layercontaining input parameters, a Kohonen layer containing Kohonen PEs, andan output layer containing the network outputs. At each PE a transferfunction with a corresponding connection weight is applied to develop arelationship between the input and output vectors. Transfer functionsmay be linear or nonlinear, however, nonlinear transfer functions arepreferred. LVQ neural networks are classification networks that classifyrelated outputs into output groups referred to as classificationoutputs. A PE group (an equal number of Kohonen PEs) is assigned to eachclassification output. Each PE group maps only to its assignedclassification output.

The BP neural network architecture used for estimating airspeed includesan input layer containing the input parameters listed in Table 1 and anoutput layer containing estimated airspeed as the single output. In thepreferred embodiment, nonlinear transfer functions are employed in thehidden layers. During network training, the input parameters are enteredinto the network and initially a random set of connection weights isapplied. The resulting network output (estimated airspeed) is comparedwith the desired output (measured reference speed) and the error(difference between estimated airspeed and reference speed) isbackpropagated through the connection weights which are adjustedappropriately. The process is iteratively repeated with new correctionweights until the error between estimated airspeed and reference speedis minimized.

The LVQ neural network architecture used to classify sideslip angleincludes an input layer containing the input parameters listed in Table1 and an output layer containing four classification outputs. As shownin FIG. 3, the four classification outputs classify sideslip angle into:(1) a forward flight (FF) classification corresponding to a sideslipangle of between 315 degrees and 45 degree (i.e., ±45 degrees from 0degree sideslip angle flight); (2) a right sideward flight (RSF)classification corresponding to a sideslip angle of between 45 degreesand 135 degrees; (3) a rearward flight (RWD) classificationcorresponding to a sideslip angle of between 135 degrees and 225degrees; and (4) a left sideward flight (LSF) classificationcorresponding to a sideslip angle of between 225 degrees and 315degrees.

The total number of PEs required in the Kohonen layer is data dependentand is generally set at a percentage of training data points employed totrain the network. One skilled in the art of neural networks maydetermine the optimum percentage. In the embodiment tested duringdevelopment of the present invention, the number of Kohonen PEscorresponds to about 10% of the number of training data points. Thus,there were 170 PEs in the OGE network and 315 PEs in the IGE network.

LVQ network training occurs in two stages. During the first stage, inputparameters are entered into the network. The network, at this point, hasa random set of connection weights. For each input parameter set, thewinning PE group (i.e., the PE group that maps most closely to theappropriate known reference output) is determined. During the firststage, the connection weights of the winning PEs are iterativelyadjusted to improve correlation between input parameters andclassification output. The first stage of training results in areasonably good classification network being developed. During thesecond stage of training, network refinement is performed. By refiningthe connection weights, miscalculations near the boundaries betweenclassification quadrants are addressed until classification errors areminimized. In the embodiment tested during development of the presentinvention, the training data set was passed through the network 45 timesbefore classification error was minimized.

During development of the present invention, two data sets weredeveloped, one for training the networks (i.e., training exemplars) andone for testing the networks. Flight test data, corresponding to thenetwork training exemplars, was collected during low airspeed tests of aNavy CH-46 helicopter at the Naval Air Warfare Center, AircraftDivision, Patuxent River, Md. The Navy CH-46 helicopter was tested atairspeeds from hover to 50 knots over a full range of sideslip angles.Data was recorded during steady flight conditions as well as duringaccelerating forward flight starting from a hover. Reference speed wasdetermined from the helicopter speed with reference to the ground andwas measured using Doppler radar. Tests were conducted only whenprevailing winds were below 5 knots to minimize uncertainty in thereference speed data. Since winds were not accounted for during theflight test, the uncertainty in reference speed data is approximately ±5knots.

Helicopter sideslip angle was derived from the Doppler velocities whichwere broken into forward and sideward velocity components. Theuncertainty of the reference sideslip angle is more significantlyaffected by prevailing winds particularly at low reference speeds.Sideslip angle uncertainty ranges from ±90 deg at 5 knots to ±5 deg at50 knots.

Fifteen input parameters, measured or determined during flight testswith the CH-46 helicopter (two engine torques were measured), were usedin developing exemplary network equations for the present invention. Thefull data base was first separated into data corresponding to steadyflight conditions and data taken during accelerating forward flightconditions. In the examples presented below, only steady flightconditions were considered. To evenly represent the domain of the lowairspeed problem, a "binning" method was developed. The data wasseparated into 36 sideslip ranges (10 deg intervals from 0 to 360 deg),10 velocity ranges (5 knot intervals, from 0 to 50 knots), and 3 grossweight ranges (high, medium, and low gross weights). Thus, the data waspartitioned into a possible 1080 bins. The training set was developed byrandomly selecting a predetermined number of data points from each bin.If a particular bin had less that the preselected quantity of datapoints, then all of the data points in that bin were selected.

The test data set consists of all data remaining in the 1080 bins afterthe training data are removed. The test data are used to evaluate thenetwork performance using data not previously encountered by the network(i.e., data it was not trained on) and, thus, provides a measure of howwell the network generalizes.

As stated earlier, low airspeed indicator input-output relationshipsvary depending on whether the helicopter is operating in ground effect(IGE) or out of ground effect (OGE). Generally, the helicopter isconsidered as operating IGE when the altitude is less than 1.5 rotordiameters. Whether the helicopter was operating IGE or OGE wasdetermined in the present case by reference to the pressure altitudemeasurement. The ground effect induces changes in static pressure whichresult in a zero or negative pressure altitude reading. Thus, a zero ornegative pressure altitude reading gives an indication that thehelicopter is operating IGE. To determine whether operation IGE or OGEsignificantly affects optimization of the neural network architectureand, thus, performance of the virtual sensor, three separate trainingand test sets were developed. The first training and test sets, referredto as the baseline data, consisted of all the steady flight conditionsavailable. The second and third training and test sets were subsets ofthe baseline data corresponding to OGE data and IGE data, respectively.

FIG. 4 represents an exemplary data set (training or test set) showingthe flight conditions at which data was collected. The radial linescorrespond to velocity in knots while the azimuthal lines correspond tosideslip angle. A zero degree sideslip angle represents forward flightwhile a 180 degree sideslip angle represents rearward flight. A 90 or270 degree sideslip angle represents right or left sideward flight,respectively. In the exemplary data set, samples were taken at a rate of10 Hz during steady flight conditions. However, the present inventionapplies equally to networks trained using data taken under differentflight conditions (e.g., accelerating flight, vertical replenishmentflight). For the present examples, there were 5582 OGE data points and8770 IGE data points.

A parametric study was conducted on the OGE data set to determine theoptimum neural network architecture for the preferred BP network usedfor estimating low airspeed. The number of hidden layers and the numberof PEs per layer was varied to determine which architecture bestestimated airspeed. The statistical parameters used to determine theoptimum architecture were the Pearson's correlation coefficient (R) andthe root mean square (RMS) error of the test data set. Pearson'scorrelation coefficient is a measure of the linearity of therelationship between estimated airspeed and measured reference speed.The RMS error provides a measure of the resulting error in airspeedpredictions when entering the test data set into the network.Performance of the neural network on the training data set willgenerally be good. Therefore, the test data set containing data notpreviously encountered by the network is used to test architectureoptimization. In the present example, the neural network was trainedusing the training data set for 640,000 iterations (i.e., the entiretraining data set was passed through the network 375 times). Every80,000 iterations the resulting network nonlinear input-outputrelationship equation was saved and evaluated using the test data set.The network was considered to be optimized when the RMS error for thetest data set stabilized. This typically occurred around 500,000iterations.

Results of the neural network architecture optimization are shown inTable 2. The preferred BP network architecture for predicting lowairspeed comprises a two hidden layer network with 25 PEs in each layer.For the preferred network architecture, the RMS error for the OGE testdata set was small and R was close to one. An alternative architecturecomprising a two hidden layer system with 65 PEs per layer produced aslightly smaller RMS error. However, this improvement was not consideredsignificant enough to warrant the added complexity of the additionalPEs.

                  TABLE 2    ______________________________________    Number of             Number of    Test Set    Hidden   PES per      RMS Error Test Set    Layers   Layer        (knots)   R    ______________________________________    1        25           3.440     0.968    1        65           2.895     0.976    2        15           2.842     0.976    2        25           2.697     0.979    2        65           2.676     0.979    ______________________________________

The nonlinear airspeed equation developed by the backpropagation neuralnetwork is: ##EQU1## where: u_(k) represents the connection weightbetween hidden layer 2 processing element k and the output (i.e.,airspeed);

v_(mk) represents the connection weight between hidden layer 1processing element m and hidden layer 2 processing element k;

w_(nm) represents the connection weight between input n and hidden layer1 processing element m; and

i_(n) represents the input parameters.

The hyperbolic tangent function (tanh) was the BP network transferfunction used in estimating airspeed. The three sets of connectionweights determine the network's success in mapping the input parametersto the output. The training process which the network undergoes adjuststhe weights. The summations from k=1 to x! and m=1 to y! depend upon thenumber of PEs chosen for each hidden layer. In the preferred network,with 25 PEs in each hidden layer, x and y are both 25. The summation n=1to z! depends upon the number of input parameters.

EXAMPLE 1

Airspeed Estimation

In accordance with the present invention, low airspeed of Navy CH-46helicopter was estimated based on the 15 input parameters and thenetwork equations learned during network training. FIG. 5, presentsresults with the optimum network architecture (i.e., 2 hidden layer BPnetwork with 25 PEs per layer) on the baseline test data set, whichincludes both IGE and OGE data. By dividing the baseline data set intotwo subsets consisting of IGE data and OGE data, it becomes evident thatground effect has a significant influence on the relationship betweenaircraft variable state parameters, as represented by the inputparameters, and estimated airspeed. As shown in FIGS. 6A (OGE trainingdata set) and 6B (OGE test data set), practicing the present inventionduring OGE flight only (i.e., using OGE data only) results insignificant improvement in estimating low airspeed. FIG. 7 shows thatmodeling airspeed during IGE flight (i.e., using IGE data only) is morechallenging. This is not unexpected, since the ground effect environmentis quite complex with unsteady flow affecting pilot controls.

To examine the degree of nonlinearity between input parameters andestimated airspeed, the network architecture with 2 hidden layers and 25PEs per layer was modified by changing the nonlinear hyperbolic tangenttransfer function of the PEs to a linear transfer function. A lineartransfer to the output was also applied. By using this technique, thenetwork becomes equivalent to a linear regression analysis. Thus, theimportance of nonlinearities in correctly modeling the low airspeeddomain can be assessed. Results of determining low airspeed using inputparameters measured during OGE flight and the linearized networkarchitecture are shown in FIG. 8. Although the linear regressiontechnique captures the general trends correctly, the present inventionwith predetermined nonlinear input-output relationship between inputparameters and airspeed is required to improve accuracy significantly.

A statistical analysis of the nonlinear neural network error indicatesthat the error is close to a normal distribution with a mean of zero.Consequently, when using a BP network architecture to predict helicopterlow airspeed, 95.5% of the data predictions will fall within ±2σ where σis the RMS error. Table 3 shows results of the test data sets for thefour cases examined.

                  TABLE 3    ______________________________________                                 Accuracy                       RMS Error ±2σ               R       (knots)   (knots)    ______________________________________    Nonlinear Network                 0.92      ±5.2   ±10.4    OGE & IGE Data    Nonlinear Network                 0.98      ±2.7   ±5.4    OGE Data    Nonlinear Network                 0.92      ±4.9   ±9.8    IGE Data    Linear Network                 0.92      ±5.7   ±11.4    OGE Data    ______________________________________

Helicopter low airspeed is predicted within ±5.4 knots when the aircraftis operating out of ground effect. This accuracy is very good given thatthe measured reference speed has an uncertainty of ±5.0 knots.

EXAMPLE 2

Sideslip Angle Classification

In accordance with the present invention, sideslip angle during lowairspeed flight of a Navy CH-46 helicopter was classified based on the15 input parameters and the network equations learned during networktraining. Sideslip angle was initially modeled using the same BP networkarchitecture as was used for airspeed predictions (i.e., the 2 hiddenlayer network with 25 PEs in each layer). However, the BP networkarchitecture was not successful for sideslip angle predictions for theOGE test data set. It was postulated that lack of correlation insideslip angle may result because the uncertainty in referencemeasurements using Doppler radar is quite high at airspeeds below 15knots. However, removing OGE data below 15 knots and retraining thenetwork did not improve accuracy.

Since the BP network produced unsatisfactory results when estimatingsideslip angle, an alternative approach was developed based onclassification of sideslip angle into four quadrants as shown in FIG. 3and discussed above. A linear vector quantization (LVQ) network waschosen. Table 4 presents results of sideslip angle classification forOGE and IGE flight conditions. Successful classification rates for eachsideslip angle quadrant and an average successful classification rate(AVE, average of the four quadrant successful classification rates) arepresented.

                  TABLE 4    ______________________________________               Successful sideslip angle               classification rate (%)               FF    RSF    RWD      LSF  AVE    ______________________________________    OGE Training Set                 98      98     99     97   98    OGE Test Set 94      94     89     80   89    IGE Training Set                 98      99     99     98   98    IGE Test Set 94      95     94     72   89    ______________________________________

Based on the premise that reference sideslip angle derived from airspeedmeasurements made below 15 knots have a high degree of inaccuracy, allinput parameters corresponding to airspeed below 15 knots (i.e., inputparameters calculated from variable state parameter data measured below15 knots) were removed and the LVQ network was retrained. Table 5presents results of sideslip angle classification for OGE and IGE flightconditions with data for reference airspeeds below 15 knots removed.

                  TABLE 5    ______________________________________              Successful sideslip angle              classification rate (%)              FF    RSF    RWD      LSF  AVE    ______________________________________    OGE Training Set                99      99     100    99   99    OGE Test Set                92      90     100    99   95    IGE Training Set                99      100    99     100  100    IGE Test Set                96      100    94     65   89    ______________________________________

Sideslip angle classification during OGE flight was significantlyimproved by using the LVQ network trained with data corresponding toairspeeds of 15 knot and greater. Average successful classificationsimproved to 95% on the test data. However, IGE test results showed nonet improvement. For OGE flight, the difficulty in classifying leftsideward flight was eliminated when below 15 knot data were removed.However, for this case, the left sideward flight classification wasworse for IGE flight. This suggests that, rather than inaccuracy inbelow 15 knot measurements, a dynamic unsteady flow region is createdduring IGE flight of the tandem rotor CH-46 helicopter that makesclassifying left sideward flight difficult.

Although specific input parameters, initial parameters, variable stateparameters, networks and network architectures were employed in thepresent examples, other input parameters, initial parameters, variablestate parameters, networks and architectures are equally applicable tothe present invention. For different classes and configurations ofhelicopters, different variable state parameters may be more easilymeasured or more applicable to measurement. Moreover, for differentclasses and configurations of helicopters, airspeed and sideslip anglemay be estimated better using different input parameters, initialparameters, variable state parameters, networks or networkarchitectures. One skilled in the arts of helicopter airspeeddetermination and of neural networks can determine which inputparameters would be most advantageous and the optimum network andnetwork architecture for predicting the desired output based on theguidance provided herein.

The advantages of the present invention are numerous. The present meansand method for estimating low airspeed and sideslip angle provide amechanically simple, inexpensive alternative to current low airspeedmeasurement technology. The neural network based means for determininglow airspeed and sideslip angle uses only helicopter variable stateparameters measured in the fixed reference frame of the helicopterfuselage. Thus, problems associated with complex and expensive methodsof transferring information from the rotating reference frame of therotors to the nonrotating reference frame of the fuselage areeliminated. Furthermore, since the input parameters for the neuralnetwork are quantities that are commonly measured by helicopter flightdata recording systems, the present invention may be easily andeconomically implemented without the added maintenance burden ofadditional sensors. The present invention is capable of improving bothmaintenance (by improving the performance of health and usage monitoringsystems) and safety for those helicopters not equipped with low airspeedmeasurement systems.

The present invention and many of its attendant advantages will beunderstood from the foregoing description and it will be apparent tothose skilled in the art to which the invention relates that variousmodifications may be made in the form, construction and arrangement ofthe elements of the invention described herein without departing fromthe spirit and scope of the invention or sacrificing all of its materialadvantages. It is therefore to be understood, the forms of the presentinvention herein described are not intended to be limiting but aremerely preferred or exemplary embodiments thereof and, within the scopeof the appended claims, the invention may be practiced other than asspecifically described.

What is claimed is:
 1. A virtual sensor for estimating low airspeed of ahelicopter comprising:determining means for determining a plurality ofinput parameters, said plurality of input parameters determined duringlow airspeed flight of the helicopter and continuously updated at asampling rate during said low airspeed flight; at least one neuralnetwork equation representative of a learned nonlinear relationshipbetween said plurality of input parameters and said airspeed; memorymeans for storing said at least one neural network equation and forreceiving said plurality of input parameters; and processing meansoperatively coupled to said memory means, said processing meansreceiving said plurality of input parameters from said memory means andproviding a low airspeed signal in response to said plurality of inputparameters and said at least one neural network equation.
 2. A virtualsensor as in claim 1 wherein said at least one neural network equationincludes at least one airspeed equation representing a nonlinearinput-output relationship between said plurality of input parameters andsaid low airspeed, said at least one airspeed equation being derived bymeans of a neural network that has been trained using training exemplarscorresponding to said plurality of input parameters and a coincidingreference speed of the helicopter, said training exemplars determined ata plurality of flight conditions representing a predefined low airspeedflight domain of the helicopter, said neural network operative fordetermining said low airspeed based upon said plurality of inputparameters.
 3. A virtual sensor as in claim 2 wherein said neuralnetwork is a backpropagation neural network.
 4. A virtual sensor as inclaim 1 wherein said memory means is at least one computer memory deviceand said processing means is a computer processor.
 5. A virtual sensoras in claim 1 wherein said determining means includes:means fordetermining a helicopter gross weight; means for determining ahelicopter center of gravity; means for determining a longitudinalcyclic stick position; means for determining a lateral cyclic stickposition; means for determining a collective stick position; means fordetermining a pilot pedal position; means for determining a pitchattitude; means for determining a roll attitude; means for determining apitch rate; means for determining a roll rate; means for determining ayaw rate; means for determining at least one engine torque; means fordetermining at least one rotor rotational speed; and means fordetermining a helicopter altitude.
 6. A virtual sensor as in claim 1wherein said determining means includes:input means for entering atakeoff weight and a takeoff center of gravity position of thehelicopter; measuring means for measuring a plurality of variable stateparameters generated during flight, said variable state parametersmeasured in a nonrotating reference frame associated with thehelicopter, wherein said plurality of variable state parameters includefuel expended during flight, longitudinal cyclic stick position, lateralcyclic stick position, collective stick position, pilot pedal position,pitch rate, roll rate, yaw rate, at least one engine torque, rotorrotational speed, and static pressure of the surrounding air; and meansfor calculating said plurality of input parameters from said takeoffweight, takeoff center of gravity position, and variable stateparameters.
 7. A virtual sensor as in claim 6 wherein said memory meansis at least one computer memory device, and said processing means andmeans for calculating said plurality of input parameters are at leastone computer processor.
 8. A virtual sensor as in claim 2 wherein saidtraining exemplars for training said neural network and said pluralityof input parameters for estimating said low airspeed are determined withthe helicopter operating in an out of ground effect flight condition. 9.A virtual sensor as in claim 1 further comprising:display meansoperatively coupled to said processing means, said display meansreceiving said low airspeed signal from said processing means andproviding an indication of said low airspeed.
 10. A virtual sensor as inclaim 1 wherein said at least one neural network equation includes atleast one sideslip equation representing a nonlinear input-outputrelationship between said plurality of input parameters and a sideslipangle of the helicopter, said at least one sideslip equation is derivedby means of a neural network that has been trained with a plurality oftraining exemplars corresponding to said input parameters a coincidingreference speed of the helicopter and a coinciding sideslip anglederived from said coinciding reference speed, said training exemplarsmeasured at a plurality of flight conditions representing apredetermined low airspeed flight domain of the helicopter, said neuralnetwork operative for determining said sideslip angle of the helicopterbased upon said plurality of input parameters.
 11. A virtual sensor asin claim 10 wherein said neural network is a linear vector quantizationneural network.
 12. A system for estimating airspeed of a helicopter ina low airspeed range of below about 50 knots in response to variablestate parameters generated during flight of the helicopter, said lowairspeed estimated in a real time fashion, said system comprising:inputmeans for entering at least one initial parameter; measuring means formeasuring, at a predetermined sampling rate, a plurality of variablestate parameters, said plurality of variable state parameters measuredin a nonrotating reference frame associated with the helicopter; meansfor calculating a plurality of input parameters based on said at leastone initial parameter and said variable state parameters, and forgenerating successive signals representing said input parameters; atleast one equation representing a nonlinear input-output relationshipbetween said input parameters and said airspeed; memory means forstoring said at least one equation and for successively receiving andstoring said signals from said determining means; and processing meansresponsive to said received signals for generating airspeed informationbased on said input parameters and said at least one equation.
 13. Asystem as in claim 12 wherein said nonlinear input-output relationshipis determined using a neural network that has been trained with trainingexemplars corresponding to said plurality of input parameters and acoinciding reference speed of the helicopter, said training exemplarsdetermined at a plurality of flight conditions representative of aflight domain experienced by the helicopter below about 50 knots.
 14. Asystem as in claim 13 wherein said neural network is a backpropagationneural network.
 15. A system as in claim 13 wherein said trainingexemplars are determined for the helicopter operating in an out ofground effect flight condition and said plurality of variable stateparameters are measured with the helicopter operating in an out ofground effect flight condition.
 16. A system as in claim 13 wherein saidmemory means is at least one computer memory device, and saiddetermining means and processing means are a computer processor.
 17. Asystem as in claim 13 wherein said at least one initial parameterincludes a takeoff weight of the helicopter and a takeoff center ofgravity position of the helicopter; andsaid measuring means includessensors for sampling said variable state parameters at saidpredetermined sampling rate, said sensors including: a sensor formeasuring fuel expended; a sensor for measuring longitudinal cyclicstick position; a sensor for measuring lateral cyclic stick position; asensor for measuring collective stick position; a sensor for measuringpedal position; at least one sensor for measuring pitch rate, roll rate,and yaw rate; at least one sensor for measuring engine torque; at leastone sensor for measuring rotor rotational speed; and a sensor formeasuring static pressure of the surrounding air.
 18. A system as inclaim 13 wherein said plurality of input parameters includes:ahelicopter gross weight; a helicopter center of gravity; a longitudinalcyclic stick position; a lateral cyclic stick position; a collectivestick position; a pilot pedal position; a pitch attitude; a rollattitude; a pitch rate; a roll rate; a yaw rate; at least one enginetorque; at least one rotor rotational speed; and a helicopter altitude.19. A system as in claim 13 further comprising:display means operativelycoupled to said processing means, said display means receiving saidairspeed information from said processing means and providing a visualindication of said airspeed.
 20. A system as in claim 19 wherein saiddetermining means and processing means is a computer processor, saidmemory means is at least one computer memory device, said input means isa computer keyboard, said display means is a computer monitor, and saidmeasuring means comprise existing flight data sensors, wherein saidcomputer processor, computer memory, computer keyboard, computer monitorand flight data sensors are part of a helicopter flight data recordingsystem onboard the helicopter.